Chords of Circles

Date: 02/28/2001 at 21:59:59
From: Robert
Subject: Chords of Circles

There is a circle with radius 10 and a chord XY 8cm long. How far is 
the chord from O, the center of the circle? 

I cannot figure out how to do it. My book has congruent chords and the 
distance to one chord, so it's in the picture and all you do is 
substitute. I do not know how to start.

Date: 02/28/2001 at 22:52:13
From: Doctor Peterson
Subject: Re: Chords of Circles

Hi, Robert.

Draw the circle and chord AB. (I'll wait while you get a pencil ...)

Okay, now draw lines from the center O of the circle to the ends of 
the chord, A and B.

Finally, draw a line from the center of the circle to the midpoint of 
the chord, C.



Now let's look at the picture. Can you see that OC is the 
perpendicular bisector of AB? That gives you a right triangle OCA. You 
know the lengths of OA and AC; Pythagoras can help you find OC.

- Doctor Peterson, The Math Forum
  http://mathforum.org/dr.math/